SMOTE Oversampling

Background

SMOTE (Synthetic Minority Over-sampling Technique) generates new minority-class samples by interpolating between existing ones along their k-nearest-neighbour edges. The classic fix for class imbalance in tabular fraud / medical screening tasks — strictly better than random duplication because it spreads the minority mass through the feature space.

Problem statement

Implement smote(X_minority, n_synth, k=5, seed=0). For each of n_synth synthetic rows:

1. Pick a random minority row $i$.
2. Find its $k$ nearest neighbours within $X_{\text{minority}}$.
3. Pick one neighbour $j$ uniformly at random from those $k$.
4. Sample $\lambda \sim \text{Uniform}(0, 1)$.
5. Synthetic row = $X_i + \lambda (X_j - X_i)$.

Input

• X_minority — np.ndarray shape $(n, d)$, the minority-class examples.
• n_synth — int >= 0, number of synthetic rows to generate.
• k — int >= 1, neighbours per source (default 5).
• seed — int, RNG seed.

Output

Returns np.ndarray shape $(n\_synth, d)$ of synthetic minority samples.

Examples

Example 1 — output shape

Input:  X=(20, 4), n_synth=50
Output: shape=(50, 4)

Example 2 — synthetic points stay in the feature range

Input:  X drawn from Uniform(0, 1)
Output: every synthetic row lies in [min - eps, max + eps] elementwise

Example 3 — reproducibility

Input:  same seed
Output: same array

Constraints

• k < n (need at least $k+1$ minority rows to find $k$ neighbours).
• Use np.random.default_rng(seed) for reproducibility.
• Returns np.ndarray of float.

Notes

• Why interpolate. Random oversampling duplicates the same points; SMOTE creates new points that fill the convex region between existing minorities — preventing the classifier from over-fitting to specific examples.
• Borderline / ADASYN. Borderline-SMOTE samples only from minorities near the decision boundary; ADASYN focuses on the hardest examples. Same kernel, different sampling weights.